where \(a_{\mu },b_{\mu },c_{\mu \nu },d_{\mu \nu },e_{\mu },f_{\mu },g_{\mu \nu \rho }\)  and \(H_{\mu \nu }\)  are indexed constants which do not transform under Lorentz transformations.
String theory [1]}, which has promise of providing a quantum theory of gravity, will lead us to a related model which will no longer be purely phenomenological. The term of interest to us is \(b_{\mu }\) which will become a quantum axion field and will also have a time-dependent background [2]}, [3]}, [4]}. In the proof of the CPT theorem it is assumed that the coupling constants are not functions of space-time. Such space-time dependent couplings can arise if there are non-trivial backgrounds of gravitational or other tensorial fields and so may lead to CPTV.The formation of such backgrounds is thus interesting.
CPT is a symmetry between particles and antiparticles and so its breaking is an issue for the understanding of baryogenesis.
